We study the case of PT-symmetric perturbations of Hermitian Hamiltonians with degenerate eigenvalues using the example of a triple-well system. The degeneracy complicates the question, whether or not a stationary current through such a system can be established, i.e.\ whether or not the PT-symmetric states are stable. It is shown that this is only the case for perturbations that do not couple to any of the degenerate states. The physical explanation for the inhibition of stable currents is discussed. However, introducing an on-site interaction restores the capability to support stable currents.
@article{arxiv.1509.07382,
title = {$\mathcal{PT}$-symmetric currents of a Bose-Einstein condensate in a triple well},
author = {Daniel Haag and Dennis Dast and Holger Cartarius and Günter Wunner},
journal= {arXiv preprint arXiv:1509.07382},
year = {2016}
}